Search for Variations of Fundamental Constants using Atomic Fountain Clocks

Abstract

Over five years, we have compared the hyperfine frequencies of ${}^{133}\mathrm{C}\mathrm{s}$ and ${}^{87}\mathrm{R}\mathrm{b}$ atoms in their electronic ground state using several laser-cooled ${}^{133}\mathrm{C}\mathrm{s}$ and ${}^{87}\mathrm{R}\mathrm{b}$ atomic fountains with an accuracy of $\sim {10}^{-15}$. These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies: $\frac{d}{dt}\ln [({\nu }_{\mathrm{R}\mathrm{b}})/({\nu }_{\mathrm{C}\mathrm{s}})]=(0.2\pm 7.0)\times {10}^{-16}{\mathrm{y}\mathrm{r}}^{-1}$ ($1\sigma$ uncertainty). The same limit applies to a possible variation of the quantity $({\mu }_{\mathrm{R}\mathrm{b}}/{\mu }_{\mathrm{C}\mathrm{s}}){\alpha }^{-0.44}$, which involves the ratio of nuclear magnetic moments and the fine structure constant.